Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory
Title GLUEBALL AND EXOTIC MESON CANDIDATES
Permalink https://escholarship.org/uc/item/4f82j1xs
Author Chanowitz, M.S.
Publication Date 1981-09-01
Peer reviewed
eScholarship.org Powered by the California Digital Library University of California V % * MASTER LBL-13398 Lawrence Berkeley Laboratory UNIVERSITY OF CALIFORNIA Physics, Computer Science & Mathematics Division
Presented at the American Physical Society 1981 Meeting of the Division of Particles and Fields, Santa Cruz, CA, September 9-11, 1981 and to be published in the Proceedings
GLUEBAI.L AND EXOTIC-MESON CANDIDATES
Michael S. Chanowitz
September 198j.
Prepared for the U.S. Department of Energy under Contract W-7405-ENG-48
DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED September 1981 LBL-13398
GLUEBALL AND EXOTIC-MESON CANDIDATES
Michael S. Chanowitz
Laurence Berkeley Laboratory and Department of Physics University of California Berkeley, California 94720
To be published in the Proceedings of the 1981 meeting
of the Division of Particles and Fields of the American
Physical Society, held at Santa Cruz, California,
September 9-11, 1981.
This work was supported by the Director, Office of Energ\
Research, Office of High Energy and Nuclear Physics,
Division of High Energy Physics of the U.S. Department of Energy under Contract W-7405-ENG-48.
Of- LNMKibuti'JN oi I,lib ..ijoi/.:.:;: .b UI.LIMITFU 2
Glueball and Exotic Meson Candidates
Michael S. Chanowitz Lawrence Berkeley Laboratory, Berkeley, California 94720
Invited talk presented at the 1981 meeting of the Division of Particles and Fields of the American Physical Snciety, Santa Cruz, California, September 9-11, 1981.
ABSTRACT
The states seen in radiative \ji decay at 1440 and 1640 MeV are discussed. It is argued that the former is almost certainly a glueball while the latter is probably either a glueball or a four quark ss(Ou + dd) state. The present status and future verification of these assignments is discussed.
I. THE GLUEBALL M.O.
I will discuss the two states seen in radiative ^ decays reported by Coyne in the preceding, very exciting talk.^ We want to consider whether they might be glueballs but first we have to examine the general problem of how to recognize a glueball. What is the experimental signature? Unfortunately the first glueball will not be delivered with a bright red glueball label. In fact, 1 believe- (see also Refs. 3 and 4) that we may have observed, but not recognized, the first glueball more than fifteen years ago in a pp annihilation experiment at CERN.-' The discoveries made in radiative v decays during the last year°>' only recently pointed clearly to this interpretation^>3 of the earlier CERN data. Quantitative theoretical understanding of the glueball spec trum is not yet at the point where predictions of masses, widths, and decay modes can serve as reliable guides. Lattice calcu lations are most promising for the future.' For my money, at present the best guide is the Bag model,-^ which Donoghue will discuss, out even this approach has serious uncertainties. For instance, the bag constant B may well be different (larger) for glueballs, glueball spin splittings are even harder to estimate because color and spin Casiir.ir values are larger for gluons, and the spherical cavity approximation is known1^ to fail in leading order. Since quantitative dynamical models are not yet able to pro vide the necessary guidance we are forced to rely on the generic, qualitative properties which a glueball must have, almosL just by definition. There are two such properties, which in police detec tive jargon I will call the glueball M.O. (modus operandil: A) Glueballs containing valence gluons will be produced prominently in hard gluon channels. B) Glueballs do not "fit"into gjq multiplets. This glueball M.O. is almost pure tautology. Indeed B) is a tau tology and A) requires only the basic notions of quantum mechanics. 3
Other conjectured properties of glueballs might be useful but are less reliable than the M.O. For instance glueballs may well couple more weakly to photons, but this issue is inextricably linked to the related questions of decay widths and mixing with qq states which are not well understood. In addition the y\ coupling of radially excited qq states may also be suppressed by a factor which we can't estimate reliably. Naively we would expect glue balls to have flavor «vmmetrir decay modes, but, as I will discuss below, this need not be true of a pseudoscalar glueball.*"* Also, Donoghue has remarked (see the discussion following his talk) that n and nT may be produced preferentially in glueball decays. In general as we depart from the M.O. the possible uncertainties and exceptions increase. Radiative 0 decays are important here because they are a prime gluebail hunt ing ground-- by modus operandus A). In perturbation theory1 -.
r(v - YX) = r(o - ygg) + o(ag) (i) where the two gluons are in a color singlet and may resonate into a glueball. Therefore any prominent new state in this channel should be examined to see if it has a plausible assignment in the qq spectrum. In the spring of 1980 the Mark II collaboration announced a large signal, seen subsequently in the Crystal Ball with a rate ~ B(< - Y(KK-). ,,) £ 4-10" , (2) and now we have word from the Crystal Ball group of a second state, seen in a weaker but very clean signal,
H B{; - Y(nn)1>w) = 5-10~ H)
In c he rest of this talk 1 wi.1 1 discuss these two st; es. I will argue that the 1440 is almost certainly a glut-ball md will discuss the future result s, exper imental and theor et ical , ohic h would allow us to delete the word "almost" from this suntt ice. For the 1640 I am less certain of an assignment. I believe it could be a glueball or a four quark state,I-5 depending oi whether B(1640 -* nn) is a small or large branching ratio.
II. E(1420) AND c;(1440)
Since the E(1420) decays to KKTT it is first necessary to consider whether it could be the state seen in y k >KK". (1420) was established in np scattering as a J*"* = 1 stat^ which t ecays to KK" predominantly via K K. But J = 1 states -ire the list we would expect to f ind stiongly produced in a two gljon chani '1, because of the Landau-Yang theorem. Motivated by :his dis< -epancy and by preliminary findings that the (RKTI)^^Q signal is Jomi- nated by 6TJ rather than K K (now confirmed by the Crystal I ill ), I reviewed the experimental record on the E(1420). The experimental picture is confusing. In np scattcri ig and pp annihilation in flight (p1An ^700 MeV.) E(1420) is pro luced LAB together with D(1285) and with o >> o , consistent with the inter pretation of D and E as approximately Ideally mixed 1=0 partners of the J c = 1' nonet. But in pp annihilation at rest where the highest statistics "E" sigi il was seen thet •? was no sign of D. In pp annihilation in flight a 5o signal for nun was observed in the E mass region, but in Tip scattering a very sensitive experiment saw no J =1 nun signal in the E region, though it did see the J™ = 1 D •* nun signal very clearly. The very high statistics
experiment in pp annihilation which first saw the (KKTI)TL/(20-40 enhancement reported a convincing spin-parity determination of J = 0~, based on the distribution in production angle. But an equally convincing CERN pion experiment ° found J = 1 . It is these most recent Tip scattering results which have led to the designation of E(1420) as an established 1+ state in the PDG tables. This i£ all summarized in Table I, where I have outlined the conclusions that can be drawn from the most reliable of the experi ments (more detail s and experimental references may be found in reference (2)).
TABLE 1: E vs.
KKTT D(1285)
K K D >> E I
(W>)
Yes l+/0" ! i) (PP) flight (£1.)
Indication "fX 6i (in) No
The reader can find other apparent inconsistencies if he scans the table, but He will also notice that the table has a consistent interpretation if two different states are involved. One is the E(1420) of the Particle Date Group table, a Jp = 1+ state which decays primarily to K K and is probably predominantly an Bs state. E(1420) does not decay strongly to nun or to 6T: . The second state. which I and the MIT group10 called G(1440),
(The final state X-s° is not allowed by Jy ?y ar.d C if C(X) = + and if X has abnormal spin-parity, j" - 0", 1 ) The initial r r J pr _j- pp state may have quantum numbers J =0 or 1 . For the dipion in an s-wave the initial pp state must be J =0 by C invariance and then only for J (X) = 0" can X be in an s-wave relative to the dipion. For J (X) = 1 either the dipion must be in (at least) a p-wave (possible for T -n but not for n^r.0) or X must be in a p-wave relative to the s-wave dipion. in either case (and especially in the latter) there is a formidable angular momentum barrier for pp annihilation at rest into E-r-n and DTITJ, which is no longer effective in X-i n~ for p ^ 700 MeV. In the XTI0^ channel we would expect the suppression of E and D to hold for larger values of p than for X" "~. The assignment j"(C) = 0~ is also suggested bv two theoretical considerations. The first^'-1^ is that the dominant partial waves for the two gluons in v ^ Vgg arc^ 0", 0 , 2 , of which only 0~ is consistent with abnormal spin-parity required by G - br . The second1*' is the special preference for KK" decays which a pseudo- scalar glueball might uniquely have, because at the quark level it would prefer annihilation to is over uu + d*d by a factor ^g/m in the amplitude (like r •+ jj\. is enhanced over T -* ev) . The ss pairs would often hadronize to s-wave KK"", which by final state inter action would form 6TT some but not all of the time. Therefore, in contrast to Ref. (13), v.e do not expect C to decay in an SU(3) symmetric fashion nor do we require the ratio G-*• K.K •" / C -> n"1*1 to correspond precisely to <: •+ KK/6 -> T\T (which is not very will known in any case). Rather the first ratio should be ===* the second and there may be more K mesons than predicted by SU(3) symmetry. These are special properties of a pseudoscalar glueball and are consistent with what is known experiraentally. The two state hypothesis is confirmed by the spin-parity result reported by Coyne,! which is entered in t IK- table. The assignment of E(1420) to the J*>C = l4"* nonet is not contro versial. We turn next tu the possible assignments of G(1440). 6
III. G(1440) and <;'(?): IS G A GLUEBALL?
Section II was devoted to the evidence that GO440) and E(1420) are different states. This section is devoted to showing that G is distinct from still another state, a pseudoscalar ?', which has yet to be discovered. ^' is the name 1 will use for the ninth member of the radially excited pseudoscalar qq nonet. Its dis covery will fill the last available slot for a qq pseudoscalar in the relevant mass range and will therefore verify modus operandus B) for the G. I will argue on the bas-i-, of what is already indicated experimentally that G does not have the properties of :/ and there fore that already the most plausible assignment is for G to be a glueball. Eight of the nine members of the radially excited pseudoscalar nonet have already been observed. They are Tt' (1270) , K ' (1400-1500), and £(12,75). The latter, ^(1275), is an unbaptized isoscalar named in honor of the ZGS where it was discovered in a very nice experiment^ which studied the reaction n~p - n7i+7r""n. This is the same high statistics experiment which observed no signal for E -+ nttTT. Data from this experiment is shown in Figure (1). D(1285) and Cf1275) are clearly visible in the IJP = 01+ and 00" 5: channels respectively. In addition there might be u small struc ture in the 00~ en channel20 near 1.4 GeV., which however depends crucially on the single low bin at 1280. If this bin were raised by only 2o the structure at 1.4 would disappear. On the other hand if the dip at 1260 is a real effect, there might be a partic1e at 1.4 GeV. which decays io tn. I will refer to this possible particle as the "glitch" or "gl(l.4)." Notice that there is no indi cation of gl(1.4) in the 00"d' channel. Finally the reader Minimi
rc* -* YC') >> r(* ->• YC) (5) 22 which in turn requireequires the mixing to be approximately singlet-octet like n' and n.
c *<;„, (6) where
Ct - 7= (uu + dd + 5s)
i (uu + dd + 25s) '7)
Next we consider the implications of singlet-octet mixing for pion scattering. Using Eqs. (6), (7) and the OIZ rule we expect'*-'
C °^> * '^ S2 (8) O(TI p •* ;n) Since nTrn is only an 012 allowed decay for the uu •+ dd components, naively we would also expect B(c' •* n"")/B(? •+ nin)=2. In fact this is probably an overestimate, because t, -*• KKTT is severely constrained by the available phase space. Assuming KKTT and HTTTT are the dominant modes (TtTtTrTt being even more suppressed by phase space) and taking account of three body phase space, I find B(£f -*• nTTTr)/B(£ -*• HTTTT) — 1.1. Then for the cross sections measured at the ZGS we expect
ot> p -»• ;'n •* nTTTrn) a 2 . . O(TT~P -*• ^n •* r\TTTm) The experimental situation appears to be quite different than Eq (9). If gl(1.4) is actually G(1440) (which, remember, we are assuming for the moment is ;') then including acceptance corrections, a rough estimate for the experimental ratio is — 0.4, a factor 5 smaller than Eq. (9). In fact the discrepancy is probably much greater, since the absence of gl(1.4) in the STT channel strongly suggests that gl(1.4) is no_t G(1440). If gl(1.4) is not G(1440) or if it is not even a real effect, then the experimental value for Eq. (9) is << .4 and the discrepancy is >> 5. The conclusion is that the hypothesis G = c' does not allow a consistent interpretation of the data from both i) •*• fX and up -*• TIT™. G(1440) is not a plaus ible partner for £(1275) in the TT' nonet. It is clearly important to reexamine the process Tip -> n^n with an experiment optimized for the G mass region. It would be best to be able to detect TITITI and KKTT in a mass range from 1.27 to 1.7 GeV. If the TT' nonet Is ideally mixed, as suggested by the coincidence of masses mc ™ m , » 1.27 GeV., then we would expect m,, - 2m , - m,. For m , between 1.4 and 1.5 GeV. , the c' would be between 1.5 and 1.7 GeV. and would decay predominantly to KKTT. Another possibility, if gl(1.4) is confirmed but established not to be the G, is that it is the (' of a non-ideal nonet. As radial excitations it is plausible that neither t, nor C are produced very strongly in i|/ •+ yX. Naively they are expected 8
at substantially smaller rates than the ground states n and n'. This is a second reason why G " c' is an implausible assignment. Assuming again that G » &', Eqs. (5) and (6) mean t' is essentially the radial excitation of n'. But we already know just from the KKTT decay ofG (compared to all decays of n') that
r(* -• YG) > r<* * vn') This is the opposite of wh*it we expect if G = c', because of the smaller available phase space for G and because the radial excitation should couple more weakly to two gluons (a la the van Royen-Weisskopf model for qq meson annihilation2^) . This remark :an be made quantitative. The rate for radiative decay of a vector quarkonium V(QQ) to a pseudoscalar quarkonium of a different flavor P(Q'Q'), V(QQ) •* y + P(Q'Q'), has been computed25 in weak binding approximation. Applied to n' and its excitation i,' the result is2° , - ,
UUJ r(u> •> Yn') UnJ\M^,l En, *n,(0)l where IC, and E are the pseudoscalar momentum and energy in the * rest frame and ^p(0) is the pseudoscalar qq wave function at the origin. If G = Z,* then Eq. (10) and the experimental inequality r(. -* fG) ^ r(0 -* YH') together imply
2 2 U-.CO)! > 3|^f(0)| (11) which makes G a most unlikely candidate to be the excitation of n ' . The argument is not complete because the binding corrections may be of the same order as the essentially kinematic factors in Eq. (10). It is important to know the approximate magnitude or even just the sign of the binding corrections. It is however reassuring that Eq. (10) gives a reasonable account of the ratio 27 2 2 P(* -> v,')/r(^ - Yn); using kn.(0)/*n(0) | = cot (ll°) , Eq. (10) gives 7 for the n' to n ratio. One specific model'-0 of c, and t, might accomodate a small ratio for o(n~p -* £fn)/a(n p •+ en) without assuming £ ' to be mostly ss. But this model predicts too large a rate for r(i(j •+ \0 and too small a rate for I'(i^ •+ yC1) if G = £' is assumed, and in the context of the model the SPEAR 1440 KKTT enhancement was initially interpreted13 as E(1420). Although I will argue in the next section that 9(1640) might be a qqqq state, this is an even less likely explanation for G than the hypothesis that G = c'- Four quark states would not be produced at larger rates than normal qq states in IJJ -+ yX. And a pseudo- scalar qqqq cannot be constructed from the orbital ground state, L = 0, but requires at 1^ast L = 1. Such states cannot easily be studied in the bag model because of the inadequacy" of the static cavity approximation for L > 0. Like the L = 0 qqqq states, x most of these states are probably too broad to be observable as ordinary resonances. 9
I have argued that G(U40) is a glueball because it is a good match to the glueball M.O. and, in particular, because it does not have the properties of the relevant qq meson, the {'. Discovery of the real c' would be the best verification of this argument. This means constructing a G — c' table, Table II, analogous to the E - G table discussed in Section II.
TABLE II: c' vs. G
KKw nirn YY/PY C(1275)
PP r ~ 80 + 10 (esp. at rest) G + £'? 6TI(+K K?)
up en? Yes VI
* - Yx 6 II 6u? No G
Kp
Right now most of Table II is empty and of the six entries, three are speculative. I have made (premature) guesses in the right column about the dominant states in each reaction. G and ^' may both appear in pp annihilation Decause of the anomalously large width and the need for Sit and K*K in the fit to the Da] itz plot.5'32 The other guesses a. d based on the preceding discussic.i. If r, and r,' are ideally mixed C' will be suppressed relative to t, in up, pp and Ify scattering but "ot in K.p scattering. Premature guesses aside, the important point is that by com pleting Table II we can disentangle G fro-n ;', including the diffi cult question of mixing. The success of the naive prediction for n' •* YY and two estimates of n" - G mixing-"3 all suggest that n' - G mixing i- small. But c.1 - G mixing could be appreciable if m - m , is very small. ^ e(1M0) <
The sign?l for i|/ -* Y(nn),,,n is clean and convincing but is significantly smaller, by an order of magnitude, than r(\fi •* Y(KKu)1 ). Consequently it is not yet clear whether the 10
glueball M.O. A) is satisfied. If the branching ratio for 8 -» nn is < 10X, then r<4> + y6) Is large, of the order of r(i£ •+ TG) , and the glueball interpretation becomes attractive. Futhermore, a statisti cal approach and experience with other hadrons of comparable mass, such as p'(1600), suggests that a branching ratio much larger than 107. for a two body mode is unexpectedly large. For instance, Bjorken's estimate-' for if •+ y + glueball •+ ynn is an order of magnitude smaller than the observed rate at 1640 because he assumed ~ IX for B(glueball •+ nn). Let's now suppose that 6 •* nn has a large branching ratio, much larger than even 10%. Then r(t|j •+ Y6) is much smaller than T(il> -*• -yG) or r(<|> -+• ynf) and more or less comparable to the ratio of more typical hadrons such as f and n. In this case 8 might have a natural interpretation as a q"q"qq state. First, this would explain the large branching ratio into a two body final state, since c|t]qq states decay predominantly by "falling apart", when they can, into two q"q mesons. Second, a typical hadronic rate for i^ •+ ye is what we naively expect for a four quark state, since the amplitudes for gg •* qq and gg •+ qqqq both begin in order 0(a ). Since 8 decays to nn, it has Jpc = 0^ + , s2++ The preference for 2++ from the Crystal Ball analysis^- is far from definitive, since it nangs on a 2a accumulation in the last angular bin. Jaffe's shopping list-1-3 of qqqq states contains many possi bilities. However it is the rare qqqq state which can give rise to an observable state; most are above their "fall-apart" threshold and are too broad to observe as ordinary reconances. ' Of Jaffe's low lying crypto-exot ic nonet, only S (980) and 6(980) are likely to be observable. S*(_980) is the clearest example: it is a (uu + dd)ss state which is below KK and nn threshold so that its width is OIZ suppressed and therefore small enough to observe. On the other hand there is no trace of Jaffe's predicted c(650) and r(900) in standard phase shif -. analyses, presumeablv because- their widths are of the order of their masses. We must therefore look for states on the shopping list which might be as narrow as the ~ 200 MeV width quoted for 6. Since the bag model estimates of the masses assume the bag ansat? and single gluon exchange, they are only semiquantitative (eg s* is predicted at 1100 MeV). Therefore I have considered all 1=0 states within 300 MeV of 1640. The J = 0 states are, in the notation of Ref. 15., Cs(36, 1550), Css(36, 1950), Cs(9 , 1800), c0(9* 1450) and C°(36* 1800). The quark contents are C = uu3d, C = (1//2)(uu + dd)Ss, and CSS = ssss. Of these Cs(36) and CSS(36)_are ruled out because they have unsuppressed fall-apart decays to (KK, nn) and nn respectively. C (9 ) is ruled out because it decays so copiously to Tin, T(rr) /r(nn) c 12, and such a large TITI signal is ruled out experi mentally. ' C (36 ) is also unlikely to be as narrow as 200 MeV because it has unsuppressed fall-apart decays to ww and ^p; for Kj - 1640 the s-wave phase space suppression is only B - .3 which is not enough to account for r — 200 MeV if the unsuppressed width is - M.. 6 Among these five J = 0 states my favorite candidate is C (9 ). If e(1640j = CS(9*) it is below threshold for its fall-apart decays. 11
K K and
r(e - K+K") = r(e •* K°K°) = r(e •+ nn). (12) Then B{9 -* nn) -y (13) and 3 r(^j -+ Y9) = (1.5) • 10" (14) 36 If 9 = C (9), it is not the state seen in yy -*• op. There are four possible J = 2 states in the 1640 ± 300 MeV. mass range. They are C°(9, 1650), C°(36, 1650), CS(9, 1950), and CS(36, 1950). C (9) and C (36) are unlikely for the same reason as the J = 0 C (36 ) discussed above: they could fall apart to ^£ and u>u> and would therefore probably be -much broader than 200 MeV. The other two states, C (9) and C (36), would have no allowed fall- apart decays if their masses were 1640 MeV. They would be below the $u: and K K thresholds and in the approximation of Ref. (15) they do not decay to two pseudoscalars. Such decays could occur by vir tue of (as yet uncalculated) gluon exchange corrections. Then as for the J = 0 C (9 ) state, KK and nn would be the dominant two body decay modes. If 8 were either the J = 2 CS(9) o- r5(36) but not both then K K , K K and nn would occur equally as in Eq. (12). But if both states were degenerate at 1640, interference effects could change the relative amounts of KK and nn. Another difference from the J = 0 CS(9*) possibility is that for these J ~ 2 states there might be a larger proportion of multibody decays, since the two body decays occur by virtue of gluonic corrections which could give rise to three body decays in the same order. Finally we cannot neglect the possibility that 6 is a garden variety qq state. There are many more such possibilities in t' s c mass range than in the mass range of the G. For instance an 1 = 1 jF _ 2++ Tyf resonance has been found at 1.7 GgV, which could be a radial excitation of the f or an L = 3 state. 3 could be an I = 0 member of one of these nonets. In this respect the 6 is J >..- ;s tightly constrained than the G whose only conceivable qq assign ment is in the nearly complete TT ! nonet. THP reasons for not preferring a qq assignment for 6 are indirect and have been alluded to above: either B(6 -+ nn) is small and r(i{> -*• ^6) is too large for an ordinary hadron, or B(6 •+ nn) is very large which is also implausible for a typical 1.64 GeV qq hadron. However it will be much harder to rule out definitively a qq assignment for 6 than for G. 12
V. CONCLUSION
G(1440) has all the properties expected of a glueball. It is the roost prominent state in a prime glueball production channel, t|i •+ yY., and it is not well accounted for as a radially excited J = 0 qq meson. Final confirmation requires the following tasks: 1) Reexamine TT p -* n^Tm to verify the indication from Ref. (18) that G is produced too weakly to be the ninth member of the J = 0 radially excited nonet. 2) Examine the strong binding corrections to ij> -> y + n'/c' to verify the nonrelativistic intuition that a radial excitation cannot be produced here with a rate ^the rate of i".he ground state. 3) Fill in the entries of Table II and thereby discover the C* and unravel the extent of c" — G mixing. In the case of 9(1640) the proper assignment is far less clear. The meson spectrum in the 1600 — 1700 GeV region is more complex and more poorly known, which means it will be harder to exclude definitively a conventional qq interpretation. Nonetheless the already known facts suggest two nonconventional interpretations: 1) If B(6 -+ nn) y6) is not unusually large. The big two body decay modes would then be naturally explained if 6 were a qqqq state. My favorite candidate is an ss(uu + dd) state which would also have large KK decay modes.
ACKNOWLEDGEMENTS
I am grateful to R. Cahn for several helpful conversations. I also wish to thank H. Lipkin and N. Stanton for useful discussions. This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract W-7405-ENG- 48. REFERENCES 1. D. Coyne, these proceedings. 2. M. Chanowitz, Phys. Rev. Lett. 4jS, 981 (1981). 3. K. Ishikawa, Phys. Rev. Lett. i_6, 978 (1981). 4. H. Fritzsch and P. Minkowski, Nuovo Cimento J30A, 393 (1975); D. Robson, Nuc. Fi.ys. B130, 328 (1977). 5. P. Baillon et. al. , Nuovo Ciraento _50A, 393 (1967). 6. D. Scharre, et al., Phys. Lett. _97_B, 329 (1980). 7. E. Bloom, Proc. 1980 SLAC Summer Inst., Ed. A. Mosher, SLAC Report 239 (1981). 8. For a recent review see M. Chanowitz, Topics in Meson Spectros copy: Quark States and Glueballs, to be published in the Proceedings of the 1981 SLAC Summer Inst. (Stanford, 1981). 9. M. Creutz, these proceeding. 13
J. Donoghue, K. Johnson, B. A. Li, Phys. Lett. j)9B, 416 (1981). J. Donoghue, these proceedings. R. Giles, unpublished (cited in Ref. 10). H. Lipkin, AKL-HEP-PR-81-23 (June, 1981). T. Appelquist et al., Phys. Rev. Lett. 34., 365 (1975); M. Chanowitz, Phys. Rev. D12, 918 (1975); L. Okun and M. Voloshin, ITEP-95 (1976), unpublished. R. Jaffe, Phys. Rev. D15, 267 (1977). C. Dionisi et al., Nuc. Phys. B169, 1 (1980). D. Scharre, Experimental Meson Spectrocopy — 1980, AIP Conf. Proc. 67, eds. S. Chung and S. Lindenbaura (AIP, N.Y., 1981), p. 329. N. Stanton et al., Phys. Rev. Lett, ftl, "ihb (1979). A. Billoire et al., Phys. Lett. 80B, 381 (1979). Here "c" denotes a fit to the 1=0 s-wave phase shift. The lightest confirmed particle in this channel is e(1400). N.Stanton, private communication. The naive arguments are very sensitive to SU(3) breaking — R. Cahn and M. Chanowitz, Phys. Lett. j>9B, 277 (197 5); H. Fritzsch and J. Jackson, Phys. Lett. 66B, 365 (1977) — but are in qualitative accord witn the data (see Ref. 17). The analogous experimental ratio for n1 and n implies 8 = -15 , in good agreement with the conventional -11 ; see K. Stanton et al., Phys. Lett. 92B, 353 (1980). R. Van Royen and V. Weisskopf, Nuovo Cimento 50A, 617 (1967). A. Devoto and W. Repko, Michigan State preprint (1981); B. Guberina and J. Kuhn, MPI-PAE/PTh 50/80 (1980). Eq. (10) is extracted from the form of the answer given by Devoto and Repko, op. cit. R. Cahn and M. Chanowitz, Ref. 22. I. Cohen and H. Lipkin, Nuc. Phys. B151, 16 (1978). Private communication to H. Lipkin from I. Cohen, cited in Ref. 13. Lipkin speculates (private communication) that a larger rate for v ~* T';1 might occur if yet higher radial excitations (3 S„) are included.
R_A Jaffe and F. Low, Phys. Rev. Dl9_, 2105_(1979). K K was invoked in Ref. 5 to explain the KK angular distribution, but the Dalitz plot (P. Baillon, Ph.D. thesis) does not have evident K bands. C. Carlson and T. Hansson, Nordita preprint, A/81; C. Rosen^-weig, A. Salomone, and J. Schechter, Syracuse Univ. preprint SU-4217-201, 7/81. J. Bjorken, Proc. 1979 SLAC Summer Inst., Ed. A. Mosher (Stanford, 1979). I assume the standard -11 n — n' mixing angle. For a discussion of the pp threshold enhancement se<- B. A. Li and K. F. Liu, SLAC-PUB-2783 (7/81).